If P= | ll 2 & 9 5 & 7 | and Q= | ll 7 & 3 4 & 1 |, find 2 P+3 Q

In a single throw of a die, find the probability of getting a number: greater than 4

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Find the locus of the centre of a circle of radius r touching externally a circle of radius R.

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Solve the inequation:

3 – 2x ≥ x – 12 given that x ∈ N.

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Prove the following identity :
$
\frac{1}{\sin A+\cos A}+\frac{1}{\sin A-\cos A}=\frac{2 \sin A}{1-2 \cos ^2 A}
$

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Perform the following operation and state the single transformation that take place :
$M_o.M_y$ on $B (4, 6)$

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Find the remainder (without division) on dividing $3x^2 + 5x – 9 by (3x + 2)$

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Find the smallest value of $x$ for which $5-2 x <5 \frac{1}{2}-\frac{5}{3} x$ where $x$ is interger

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When $x^3+2 x^2-k x+4$ is divided by $x – 2$, the remainder is $k.$ Find the value of constant $k.$

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If $A =\left|\begin{array}{l}1215 \\ 1117\end{array}\right|$ and $B =\left|\begin{array}{ll}2 & 7 \\ 4 & 9\end{array}\right|$ find $A -2 B$

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If $a: b=4: 7$, find the following:
$\frac{6 a-b}{a+3 b}$

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Answer